Polarization Charge around Impurities in Strained and Tilted 2D Dirac materials

We demonstrate that uniaxial strain, as well as the cone tilt naturally present in certain 2D Dirac materials, introduces quasiparticle anisotropy that has a profound effect on the polarization charge induced by external impurities (both Coulomb and short-range). For example, the charge distribution induced by a Coulomb impurity exhibits an unconventional power law tail along with a strain-dependent admixture of angular harmonics. Analytical results were obtained in the continuum limit via perturbation theory valid for weak (subcritical) potentials, and supported by numerical lattice simulations based on density-functional theory. The presence of distributed charge is in sharp contrast to the response in pristine graphene, where the polarization charge is fully localized at the impurity position. Thus measurements of the charge response reflecting this novel behavior may be used to extract information about the mechanical and electronic properties of a sample.